MATHEMATICAL MODELLING Series 2
The maths behind the traffic jam!
Mathematics and applied mathematics are used in everyday life. Stock markets, mobile phones, car manufacturing, Google, Hollywood special effects, digital TV
and satellites all use cutting-edge mathematics tools in their basic functions. The Mathematical Modelling Series presents a number of applications of mathematics
in domains as varied as the human body, volcanology, telecommunications or finance.
Have you ever been stuck in a traffic jam?
suddenly as you came to a
How often is your bus late? What’s the quickest route across town?
halt, you move off again
Delays due to traffic are a regular annoyance in day-to-day life, but the
with a clear road ahead.
real problem is much bigger. The combined effect of people being late
There’s no accident or any
for work, goods being delivered after they’re due and buses, trains and
other cause, so what just
planes running behind schedule costs people billions of Euro each year.
happened? A phantom jam,
So do we know what causes traffic jams? Can we predict when and
that’s what. The cause seems
where they’re going to happen? Is it possible to eliminate delays for
unlikely: suppose in heavy
good? These questions have interested scientists and engineers for
traffic someone brakes a little too hard. Imagine then that each person
decades, and the answers lie in mathematics.
after also brakes a little too hard until somewhere further down the
line of cars, people are forced to come to a complete stop.
How it works
Traffic is something we experience in everyday life but
few people realise that mathematics can be used to
explain many of its essential features. Similar
phenomena occur in a range of applications,
e.g., pedestrians on streets, the internet,
schools of fish, or trails of ants. Traffic is
Conclusion
There are many interesting and important aspects of
transportation and traffic flow. Mathematics is essential if
we want to increase the efficiency of our transportation
systems. Mathematics will have a dramatic effect on
the way we travel in the future.
everywhere! On busy roads, a strange
phenomenon is plaguing motorists around
the world. Picture yourself driving down a clear
stretch of road. Suddenly you come to a
complete standstill in a queue of traffic. You
Parts of the curriculum used in this project
n Matrices
n Linear equations
n Sequences and series n Statistics
n Differential equations
remain stationary for several minutes until, just as
ACKNOWLEDGEMENTS AND MORE INFORMATION
This research is supported by the Mathematics Application Consortium
for Science and Industry (MACSI) funded by the Science Foundation
Ireland Mathematics Initiative Grant 06/MI/005.
If you want more information about MACSI and this project:
• Contact Martina O’Sullivan (project facilitator) –
[email protected]
• Visit the MACSI website – www.macsi.ul.ie.